I am measuring the resistivity of the sample using the four probe measurement. My electrodes are rectangular (1mm*5mm )shaped platinum (50nm thickness) deposited on top of the sample separated by 1mm width . Considering the penetration depth of the sample, Which area should i choose as the Area for the resistivity calculations. Should i use the entire base area of the sample (could have shorter current penetration depth), Or should i use the Area of the current electrode ( considering the current Penetration depth ) for accurate calculation !!!
Do you use the parallel plate configuration?
In that case it's the area covered by one electrode.
http://en.wikipedia.org/wiki/Capacitor#mediaviewer/File:Parallel_plate_capacitor.svg
Hello Saj,
your electrodes are quite big, compared to the needles used in your reference. In that case my approach would be the following:
The penetrated volume would be limited by the thickness of your sheet (t = 1 mm), the width of your electrode (w = 5 mm) and the space between your electrodes (V high and V low, s = 1 mm).
The penetrated distance in this case would be the space between your electrodes (s). So the penetrated area (A) should be the thickness of your sheet multiplied with the width of your electrodes (t * w). For this "volume factor" (or cell constant, K) you divide the area by distance:
K = A / s = (t * w) / s
Calculate the specific resistivity (Rsp.) by multiplying the measured resisitvity (Rm.) with (K).
That means: Rsp. = Rm. * K = Rm. * (A / t)
How about that?
Dear Saj Maohan,
yours is a "classical" problem when the four-probe technic is used in parctice.
You are in the condition in which the sample thickness t (1 mm) is neither so "small", nor so "big" in comparison to the electrode distance d (1 mm); they are the same.
So you cannot consider your measurement as a superficial measurement (td).
In both mentioned cases you can largely simplify the equation (tickness limited in the first case, electrode spacing limited in the latter one).
So. What to do?
You can simply refers to correction factors you find in the literature. In your case for t=d you have about the 72% of the resistance you would obtain with a bulk meaurement:
2*3.14*d*V/I so
you have 4.52 * d * V/I.
Please refer to the original work on sheet resistance measurements (F. S. Smits, "Measurement of sheet resistivities with the four point probe", The Bell System Technical Journal, 1958) and also to this site
http://four-point-probes.com/four-point-probe-theory/
where you surely find useful information.
Hoping to be helpful,
sincerely,
§
I agree with Prateek. Resistivity is sheet resistance multiplied by the film thickness and its expressed as ohm.cm. You only require area when you want to determine resistance which is simple the resistivity x length of electrode all divided by the electrode cross-sectional area.
I would advice you to characterize your electrodes first by depositing them on glass substrate or Si with oxide spacer layer of 25 nm or greater.,otherwise your sheet resistance values will be inaccurate if your electrodes are on a conducting material.
If your question is about how to calculate sheet resistance which is different from resisitivity, then follow Stefano's recommendation.
How thick is the sample that you are measuring? And how wide is the sample? If you want the sample resistance exactly, it can make a lot of difference. I agree with Gwamuri that you should characterize your electrodes by measuring them on an insulating substrate (another 4 point measurement, but you should be able to use metallic probes...you only need an approximate value for the Pt contact resistance). It should be much smaller than the sample resistance. It would be helpful to give the sample resistance value that you have measured so far.
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